Generalization of soft $\mu $-compact soft generalized topological spaces

TL;DR

This paper introduces and explores the concept of soft nearly μ-compact spaces, generalizing soft μ-compact spaces within soft generalized topology, and investigates their properties and relationships.

Contribution

It defines soft nearly μ-compact spaces, analyzes their properties, and shows how they generate parametrized families of nearly μ-compact spaces, extending the theory of soft topological spaces.

Findings

Soft nearly μ-compact spaces are introduced and characterized.

A soft nearly μ-compact space produces a parametrized family of such spaces.

Counterexamples demonstrate that the converse of the main property does not hold.

Abstract

Our work aims to introduce generalization of soft $ \mu $-compact soft generalized topological spaces, namely; soft nearly $ \mu $-compact spaces which are defined over initial universe with a fixed set of parameters. Basic properties and some significant corollaries will be introduced, Moreover, we investigated that a soft nearly $ \mu $-compact space produces a parametrized family of nearly $ \mu $-compact spaces. Some counter examples will be established to show that the converse may not be hold.